While moving arm, leg mesh messes up
You have not properly assigned weights to your lowerarm. Select this bone in Pose Mode, then select the character mesh and press Ctrl+Tab to enter the Weight Paint Mode. Set the Weight factor in a Tool Shelf (T) to 0.000. Now select every single bone of the hand and see if there are weights assigned to the rest of the body and remove them (paint them, so they're blue).

NOTE 1: I haven't removed all the weights- it's just an example.

NOTE 2: The armature in my .giff is a bit off, since I'm using the older version of Blender than yours.